Efficient Optimization and Robust Value Quantification of Enhanced Oil Recovery Strategies

With an increasing demand for hydrocarbon reservoir produces such as oil, etc., and difficulties in finding green oil fields, the use of Enhanced Oil Recovery (EOR) methods such as polymer, Smart water, and solvent flooding for further development of existing fields can not be overemphasized. For reservoir profitability and reduced environmental impact, it is crucial to consider appropriate well control settings of EOR methods for given reservoir characterization. Moreover, finding appropriate well settings requires solving a constrained optimization problem with suitable numerical solution methods. Conventionally, the solution method requires many iterations involving several computationally demanding function evaluations before convergence to the appropriate near optimum. The major subject of this thesis is to develop an efficient and accurate solution method for constrained optimization problems associated with EOR methods for their value quantifications and ranking in the face of reservoir uncertainties. The first contribution of the thesis develops a solution method based on the inexact line search method (with Ensemble Based Optimization (EnOpt) for approximate gradient computation) for robust constrained optimization problems associated with polymer, Smart water, and solvent flooding. Here, the objective function is the expectation of the Net Present Value (NPV) function over given geological realizations. For a given set of well settings, the NPV function is defined based on the EOR simulation model, which follows from an appropriate extension of the black-oil model. The developed solution method is used to find the economic benefits and also the ranking of EOR methods for different oil reservoirs developed to mimic North Sea reservoirs. Performing the entire optimization routine in a transformed domain along with truncations has been a common practice for handling simple linear constraints in reservoir optimization. Aside from the fact that this method has a negative impact on the quality of gradient computation, it is complicated to use for non-linear constraints. The second contribution of this thesis proposes a technique based on the exterior penalty method for handling general linear and non-linear constraints in reservoir optimization problems to improve gradient computation quality by the EnOpt method for efficient and improved optimization algorithm. Because of the computationally expensive NPV function due to the costly reservoir simulation of EOR methods, the solution method for the underlying EOR optimization problem becomes inefficient, especially for large reservoir problems. To speedup the overall computation of the solution method, this thesis introduces a novel full order model (FOM)-based certified adaptive machine learning optimization procedures to locally approximate the expensive NPV function. A supervised feedforward deep neural network (DNN) algorithm is employed to locally create surrogate model. In the FOM-based optimization algorithm of this study, several FOM NPV function evaluations are required by the EnOpt method to approximate the gradient function at each (outer) iteration until convergence. To limit the number FOM-based evaluations, we consider building surrogate models locally to replace the FOM based NPV function at each outer iteration and proceed with an inner optimization routine until convergence. We adapt the surrogate model using some FOM-based criterion where necessary until convergence. The demonstration of methodology for polymer optimization problem on a benchmark model results in an improved optimum and found to be more efficient compared to using the full order model optimization procedures

Adaptive machine learning-based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery

In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer flooding. The computational approach is based on an adaptive training procedure of a neural network that directly approximates an input-output map of the underlying PDE-constrained optimization problem. The training process thereby focuses on the construction of an accurate surrogate model solely related to the optimization path of an outer iterative optimization loop. True evaluations of the objective function are used to finally obtain certified results. Numerical experiments are given to evaluate the accuracy and efficiency of the approach for a heterogeneous five-spot benchmark problem.publishedVersio

A theoretical look at ensemble-based optimization in reservoir management

Ensemble-based optimization has recently received great attention as a potentially powerful technique for life-cycle production optimization, which is a crucial element of reservoir management. Recent publications have increased both the number of applications and the theoretical understanding of the algorithm. However, there is still ample room for further development since most of the theory is based on strong assumptions. Here, the mathematics (or statistics) of Ensemble Optimization is studied, and it is shown that the algorithm is a special case of an already well defined natural evolution strategy known as Gaussian Mutation. A natural description of uncer-tainty in reservoir management arises from the use of an ensemble of history-matched geological realizations. A logical step is therefore to incorporate this uncertainty description in robust life-cycle production optimization through the expected objective function value. The expected value is approximated with the mean over all geological realizations. It is shown that the frequently advocated strategy of applying a different control sample to each reservoir realization delivers an unbiased estimate of the gradi-ent of the expected objective function. However, this procedure is more variance prone than the deterministic strategy of applying the entire ensemble of perturbed control samples to each reservoir model realization. In order to reduce the variance of the gradient estimate, an importance sampling algorithm is proposed and tested on a toy problem with increasing dimensionality.acceptedVersio

Multiobjective and Level Set Methods for Reservoir Characterization and Optimization

Proper management of oil and gas reservoirs as dynamic systems reduces operational expenditures, alleviates uncertainty, and increases hydrocarbon recovery. In this dissertation, we focus on two issues in reservoir management: multiobjective integration and channelized reservoir calibration. Multiple objectives, including bottom-hole pressure (BHP), water cut, and 4-D seismic data, are utilized in model ranking, history matching, and production optimization. These objectives may conflict, as they represent characteristics coming from different measurements and sources, and, significantly, of varying scales. A traditional weighted-sum method may reduce the solution space, often leading to loss of key information for each objective. Thus, how to integrate multiple objectives effectively becomes critical in reservoir management. This dissertation presents a Pareto-based approach to characterize multiobjective and potentially conflicting features and to capture geologic uncertainty, preserving the original objective space and avoiding weights determination as in the weight-sum method. For channelized reservoirs, identification of the channel geometry and facies boundaries, as well as characterization of channel petrophysical properties are critical for performance predictions. Traditional history matching methods, however, are unable to preserve the channel geometry. We propose a level set based method, integrated with seismic constraint and coupled with the Grid Connectivity Transform (GCT) for channelized reservoirs calibration. We first develop the Pareto-based model ranking (PBMR) to rank multiple realizations, taking into consideration seismic and production data. We demonstrate that this approach can be applied to select multiple competitive realizations compared with the weighted-sum method, and uncertainty range of each objective can be effectively addressed. Next, we extend the Pareto-based framework to full-field history matching and production optimization of the Norne Field in the North Sea. A hierarchical history matching workflow including global and local updates helps to capture the large- and fine-scale heterogeneity. A two-step polymer flood optimization consisting of the streamline-based rate optimization and the Pareto-based polymer optimization is shown to be beneficial for reducing the impact of heterogeneity and increasing production improvement as well as NPV. Finally, we propose a two-step history matching workflow for facies and property calibration of the channelized reservoirs, where the channel geometry is modeled using the level set method, and smaller scale heterogeneity is modeled using the GCT. Moreover, the seismic constraints incorporated into the level set improves facies model calibration

공정시스템의 이산화탄소 배출 및 에너지 소모 절감을 위한 의사결정 절차에 관한 연구

학위논문 (박사)-- 서울대학교 대학원 : 화학생물공학부, 2012. 8. 윤인섭.본 논문은 화학공정 시스템의 이산화탄소 배출과 에너지 소모 절 감을 위한 의사결정 절차를 제안하고 여러 사례 연구를 다루고 있다. 지금까지 대부분의 화학공정은 비용의 효율 측면에서 최적화가 이 루어졌고, 이를 바탕으로 설계, 개선되었다. 하지만 전 세계적으로 온실가스 규제, 에너지 사용절감 등 공정의 환경적인 측면의 제약이 많아짐에 따라, 화학공정의 운영은 더이상 비용이나 제품의 효율적인 측면만 중시할 수 없는 상황이 되었다. 그러므로 화학공정의 지속가 능한 발전은 불가피한 것이 되었다. 지속가능한 발전을 위해 시스템 측면에서 의사결정이 필요한 몇 가지가 있는데, 원료의 선택, 공정 계 획, 공정 운영 등을 들 수 있다. 그래서 도입할 수 있는 방법이 전과정평가인데, 전과정 평가는 환경적으로 건전하고 지속가능한 발전을 실현하기 위해 원료, 제조, 유통, 소비, 폐기로 인한 자원, 에너지 소비 및 환경오염 부하를 최소화시키고 개선방안을 모색하는 방법이다. 기존의 전과정 평가는 하나의 제품에 국한되었던데 반해, 본 논문에서는 화학공정의 전과정을 범위로 설정하여 에너지 및 비용 뿐만 아니라 이산화탄소 배출과 같은 환경적인 요소를 고려할 수 있게 하였다. 먼저, 전과정 평가에 대한 설명 및 기본 구조를 살펴보도록 한다. 그리고 지속가능성을 위해 전과정 평가를 이용한 절차와 최적 의사결정에 미치는 영향에 대해 살펴보았다. 전과정 평가는 목적과 범위의 설정이 중요한데, 본 논문에서 다루는 전과정 평가의 목적은 이산 화탄소 배출량 에너지 사용의 최소화이다. 전과정의 범위는 각 사례 공정을 적절히 한정하였다. 그리고 전과정 평가의 범위에 포함되는 공정은 상용 공정 모사기와 수치해석적인 방법을 이용하여 구현하였 다. 다음으로 공정의 전과정에 존재할 수 있는 불확실성을 고려하기 위해 몬테카를로모사기법을 적용하였다. 이는 전과정평가의 신뢰성 있는 결과를 얻기 위해 수행되었다. 특히 화학공정에서의 의사결정 은 불확실성을 자연적으로 내포하고 있기 때문에, 기존의 확정적인 모델과 달리 확률적 모델을 이용하는 것이 더 나은 결과를 얻을 수 있게 한다. 최적 운영 및 관리를 위한 접근방법으로는 근사 동적 계획법을 사용하였다. 기존의 동적 계획법이 차원수의 급격한 증가로 인해 계산하는데 어려움이 있는데 반해,근사동적계획법은 계산해야할 차원수를 줄여 최적의 해를 찾는 방법으로 공정의 생산계획이나 일정관리, 원료의 배치 등에 유용하게 쓰일 수 있다. 특히 실제 화학공정에서는 차원수가 무한히 증가할 수 있으므로 근사 동적 계획법을 이용하여 차원수를 줄이는 것이 필요하다. 하지만 기본적인 근사 동적계획법 또한 각 상태의 값을 구하는 절차에서 다음 상태로의 기대값의 최적 화를 수행해야하기 때문에 계산하기 힘든 단점을 갖고 있다. 이러한 단점을 극복하기 위해 결정 후 상태에 기반한 근사 동적 계획법을 이 용하였다. 위 연구에서 제안된 절차는 사례 연구를 통해 그 효용성을 입증한다. 첫번째 사례연구는 디메틸에테르 공정을 위한 원료 결정이다. 디메틸에테르는 전도유망한 신재생에너지로서 여러 원료를 이용해 합성할 수 있다. 이에 각 원료를 얻는 것으로부터 디메틸에테르를 합성하는 공정까지의 전과정을 상용 공정 모사기로 모사하였고, 그 전과정에 대해 이산화탄소와 에너지 효율 측면에서 영향평가를 수행 하였다. 두번째 사례연구는 에너지 시스템의 생산계획 결이다. 불확 실성을 가지는 미래 에너지 생산계획의 예측을 위해 확률적 모델을 기반으로 최적화를 수행하였다. 그 결과, 향후 각 에너지 생산계획의 범위를 제시하였고 불확실성 인자들의 민감도를 분석하였다. 세번째 사례연구는 이산화탄소 지중저장 및 원유 회수증진 공정 운영방법 결정이다. 이산화탄소 처리 방법 중 하나인 지중저장을 단순히 저장 에 국한하지 않고 원유 회수증진에 이용하여 보다 지속가능한 발전을 모색하고자 한다. 여러 포집원에서 포집된 순도 높은 이산화탄소는 원유 회수증진에 매우 유용하게 사용될 수 있으며, 사례연구를 통해 원유 회수증진과 지중저장 사이에서 지속가능한 운영 전략을 제시하 여 이산화탄소 처리 및 저장에 대한 의사결정을 지원하였다.Abstract i Chapter 1 Introduction 1 1.1 Life cycle assessment . . . . . . . . . . . . . . . . . . . . 2 1.2 Sustainable development and sustainability . . . . . . . . 8 1.3 Proposed procedures for decision making . . . . . . . . . 11 1.4 Research scope . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Outline of thesis . . . . . . . . . . . . . . . . . . . . . . . 17 Chapter 2 Background Theory 19 2.1 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . 19 2.2 Finite volume method . . . . . . . . . . . . . . . . . . . 29 2.3 Approximate dynamic programming . . . . . . . . . . . . 33 2.3.1 Introduction to dynamic programming . . . . . . 33 2.3.2 The three curses of dimensionality . . . . . . . . . 38 2.3.3 Introduction to approximate dynamic programming . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.3.4 Approximate dynamic programming using postdecision state variable . . . . . . . . . . . . . . . 47 Chapter 3 Evaluation of Raw Materials for DME Production System 51 3.1 Problem description . . . . . . . . . . . . . . . . . . . . . 51 3.2 Life cycle assessment of DME production system . . . . . 55 3.2.1 Goal and scope definition . . . . . . . . . . . . . 55 3.2.2 Inventory analysis . . . . . . . . . . . . . . . . . . 58 3.3 Results and impact assessment . . . . . . . . . . . . . . . 79 3.4 Cost analysis . . . . . . . . . . . . . . . . . . . . . . . . 83 Chapter 4 Energy Planning Model Considering Uncertainties 87 4.1 Problem description . . . . . . . . . . . . . . . . . . . . . 87 4.2 Mathematical modeling . . . . . . . . . . . . . . . . . . . 91 4.2.1 Definition of production costs . . . . . . . . . . . 91 4.2.2 Learning effects . . . . . . . . . . . . . . . . . . . 93 4.2.3 Fuel and carbon prices for handling uncertainties 96 4.2.4 Monte Carlo simulation . . . . . . . . . . . . . . 97 4.3 Structure of the proposed model . . . . . . . . . . . . . . 98 4.3.1 Structure of the problem . . . . . . . . . . . . . . 98 4.3.2 Optimization of energy planning . . . . . . . . . . 100 4.4 Results and their implications . . . . . . . . . . . . . . . 106 Chapter 5 Optimal Management for CO2 Enhanced Oil Recovery 113 5.1 Problem description . . . . . . . . . . . . . . . . . . . . . 113 5.1.1 Enhanced oil recovery (EOR) . . . . . . . . . . . 115 5.1.2 Basics of reservoir modeling . . . . . . . . . . . . 117 5.2 Numerical modeling: two point flux approximation . . . . 124 5.3 Numerical modeling: miscible flow . . . . . . . . . . . . . 129 5.3.1 Pressure change . . . . . . . . . . . . . . . . . . . 129 5.3.2 Saturation change . . . . . . . . . . . . . . . . . . 133 5.4 Optimal management of the CO2-EOR . . . . . . . . . . 137 5.4.1 Selection of feasible reservoir for CO2-EOR . . . . 139 5.4.2 Numerical results of reservoir modeling . . . . . . 142 5.4.3 The calculation of the amount of CO2 . . . . . . 149 5.4.4 The calculation of energy requirement . . . . . . 157 5.5 Results and their implications . . . . . . . . . . . . . . . 163 Chapter 6 Conclusion 173 Bibliography 177Docto

Development of cost-effective surfactant flooding technology. Final report

Task 1 of this research was the development of a high-resolution, fully implicit, finite-difference, multiphase, multicomponent, compositional simulator for chemical flooding. The major physical phenomena modeled in this simulator are dispersion, heterogeneous permeability and porosity, adsorption, interfacial tension, relative permeability and capillary desaturation, compositional phase viscosity, compositional phase density and gravity effects, capillary pressure, and aqueous-oleic-microemulsion phase behavior. Polymer and its non-Newtonian rheology properties include shear-thinning viscosity, permeability reduction, inaccessible pore volume, and adsorption. Options of constant or variable space grids and time steps, constant-pressure or constant-rate well conditions, horizontal and vertical wells, and multiple slug injections are also available in the simulator. The solution scheme used in this simulator is fully implicit. The pressure equation and the mass-conservation equations are solved simultaneously for the aqueous-phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used that greatly reduce numerical dispersion effects. Task 2 was the optimization of surfactant flooding. The code UTCHEM was used to simulate surfactant polymer flooding

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008